Consistency of Heyting arithmetic in natural deduction | Zendy

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Consistency of Heyting arithmetic in natural deduction

Author(s) -

Kanckos Annika

Publication year - 2010

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200910118

Subject(s) - falsity , mathematics , consistency (knowledge bases) , natural deduction , reduction (mathematics) , interpretation (philosophy) , natural number , discrete mathematics , arithmetic , algebra over a field , pure mathematics , computer science , programming language , epistemology , philosophy , geometry

A proof of the consistency of Heyting arithmetic formulated in natural deduction is given. The proof is a reduction procedure for derivations of falsity and a vector assignment, such that each reduction reduces the vector. By an interpretation of the expressions of the vectors as ordinals each derivation of falsity is assigned an ordinal less than ε 0, thus proving termination of the procedure (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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